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Simplifying p2 + 24p = 49 Reorder the terms: 24p + p2 = 49 Solving 24p + p2 = 49 Solving for variable 'p'. Reorder the terms: -49 + 24p + p2 = 49 + -49 Combine like terms: 49 + -49 = 0 -49 + 24p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + 24p + 49 + p2 = 0 + 49 Reorder the terms: -49 + 49 + 24p + p2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 24p + p2 = 0 + 49 24p + p2 = 0 + 49 Combine like terms: 0 + 49 = 49 24p + p2 = 49 The p term is 24p. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24p + 144 + p2 = 49 + 144 Reorder the terms: 144 + 24p + p2 = 49 + 144 Combine like terms: 49 + 144 = 193 144 + 24p + p2 = 193 Factor a perfect square on the left side: (p + 12)(p + 12) = 193 Calculate the square root of the right side: 13.892443989 Break this problem into two subproblems by setting (p + 12) equal to 13.892443989 and -13.892443989.Subproblem 1
p + 12 = 13.892443989 Simplifying p + 12 = 13.892443989 Reorder the terms: 12 + p = 13.892443989 Solving 12 + p = 13.892443989 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + p = 13.892443989 + -12 Combine like terms: 12 + -12 = 0 0 + p = 13.892443989 + -12 p = 13.892443989 + -12 Combine like terms: 13.892443989 + -12 = 1.892443989 p = 1.892443989 Simplifying p = 1.892443989Subproblem 2
p + 12 = -13.892443989 Simplifying p + 12 = -13.892443989 Reorder the terms: 12 + p = -13.892443989 Solving 12 + p = -13.892443989 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + p = -13.892443989 + -12 Combine like terms: 12 + -12 = 0 0 + p = -13.892443989 + -12 p = -13.892443989 + -12 Combine like terms: -13.892443989 + -12 = -25.892443989 p = -25.892443989 Simplifying p = -25.892443989Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.892443989, -25.892443989}
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